Trautman–Bondi mass and angular momentum for scalar field and gravity

Abstract. The energy and angular momentum at null infinity are presented with the help of a simple example of a massless scalar field in Minkowski spacetime. It turns out that the case of the massless scalar field in Minkowski spacetime already exhibits all the essential features of the problem at hand, while avoiding various technicalities which arise when one wishes to describe Einstein gravity. In General Relativity we present a new variational formulation on hypersurfaces which are space-like inside and light-like near future null infinity. The formulae, we obtain, correspond to the mass loss formula